As it turns out, this vector field can be identified as the Killing vector field \(v\)  emerging from the superalgebraMore precisely, in the following we use the vector field that enters in the definition of \(P^+_\omega \)  which does not necessarily have to be \(v\) . However, both choices yield isomorphic subbundles of \(\Omega ^2\)  [1]}..
as–main implies that we obtain \([\sigma _\omega ]\in K_H(T_HX)\)  as
\([\sigma _\omega ]=[0]+\theta _2[\sigma _\omega |_Y]\in K_H(T_H(X-Y))\oplus \theta _2K_H(TX|_Y),\) 
